Molecular Dynamics simulations of a model bilayer made of surfactant dimers in a Lennard-Jones solvent are reported for three sizes of the systems up to an area of $100\sigma \times 100\sigma$ and for a large interval of specific areas:from hole formation under tension to the floppy state of a compressed bilayer. The transition to the floppy state appears quite abrupt and discontinuous; in the floppy state the lateral tension is negative. Lateral tension and the structure factor were determined for all 3 sizes and all areas; the apparent rigidity constant and apparent surface tension are determined and correlated with the specific area and the finite size. The replacement of the $1/q^2$ capillary-wave divergence by a pole is accounted for and explained. The derivative of the lateral tension jumps from a high value in a flat bilayer to a low value in the floppy, rough, and buckling state, where the tension itself is negative.